As Yvonne said, his death certificate should give the name of the cemetery where he was buried.It also should show his "usual residence" and the name and address of the informant, too.If the informant was a relative it might give that relationship, but not always.This would be someone you might track down, see if they know more about Arthur.
You want that residence, because a person's death is recorded where they were they died, and it can be some place other then where they lived, and might be buried.Once you know for sure where he lived, look for an obituary, too.Survivors are often listed, and if Arthur remarried, members of his second family might be listed.A good way to pick up married names of female members of a family, too.
Depending on how long they were married, he might have applied for his Soc Sec card after the divorce.A copy of his SS application will give his residence at the time of his application and other data, too.
He shows up on the SSDI, which means he was receiving SS benefits.Since he was only 56 at the time of his death, he must have been receiving disability benefits.
Shaver, Arthur, b 12 Nov 1912; d Feb 1968; last residence not shown on the index; SS card was obtained in TX.
You only asked for info on Arthur after the divorce, have you gone back up his family tree?You might find descendants of siblings etc that might know about him.
1910 census Upshur Co, TX:
Shaver, John W., h, 60, M(1) 43 yrs, b LA, KY, TX
" Rachel , w, 55, M(1) 43 yrs, 11 ch, 3 lvg, b LA, KY, CT
" Lacy, s, 19, b TX
" ____, d, 13, b TX
1920 census Wood Co, TX:
Shaver, John W., h, 68, md, b LA, TX, TX
" Rachel K., wf, 62, md, b LA, TX, CT
1880 census Wise Co, TX:
Category: Name:Relationship to head of household; Marital Status; Gender; Race; Age; Birthplace; Occupation; Father's Birthplace; Mother's Birthplace.
John W. SHAVERSelfMMaleW35LAFarmerTXTX
Rachel SHAVERWifeMFemaleW28LAKeeping HouseKYKY
1870 census Lamar Co, TX:
Shaver, John W., 25, b LA
" Rachel C., 18, b LA
" Elizabeth, 2, b TX
" William E., 1, b TX
These census records give you John's middle name, Wesley, and Rachel's middle initial is K and C, I'm willing to bet her middle name is Katherine or Catherine.
Happy Hunting (^_^)